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NOTES FOR 
MECHANICAL DRAWIHO 



FRANK L MATHEW50K 






Class _ '1^3 
Book 



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GopyriglitN" 

COPYRIGHT DEPOSIT. 



NOTES FOR 
MECHANICAL DRAWING 



Arranged for the use of the students of 

THE MECHANIC ARTS HIGH SCHOOL 
and THE EVENING SCHOOL OF TRADES 

by 

FRANK E. MATHEWSON 



' > > ■> 

t S ) 3 3 



Springfield , Massachusetts 
1904 



LIBRARY of CONGRESS 
Two Cvpies Received 

JAN 22 1904 

V Copyiight Entry 
CLASS "^ XXc. No. 

n h I ^■ 

' COPY B 






Notes for Mechanical Drawing 

Copyrighted, January 2, 1904 

by Frank E. Mathewson 



9 "^^ ""tS t«« cs 



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TMP96-024382 



PREFACE 

The Notes for Mechanical Drawing are the results of twelve 
years experience in teaching high school and evening classes, 
arranged to cover the subjecft from a pradtical point of view 
suggested by the careful observation of the needs of these 
classes. The book is not a text-book, but is simply a collecft- 
ion of notes, exercises, and problems, to be used in connection 
with such explanation or demonstration as, in the judgment 
of the instrudtor, seems best suited to the classes. 

January 1, 1904 Frank E. Mathewson. I 



MECHANICAL DRAWING 1 

MARGINS :- Tack the paper on the drawing board, and draw marginal lines as shown in 
the drawing below, obtaining a working space of 9" X 12''- Use the T square for all hori- 
zontal lines, and the triangles in connection with the T square, for all vertical lines, and lines 
at 15°, 30°. 45°, 60°, and 75°. 




MECHANICAL DRAWING 

LETTERING. H Is important that all lettering should be done quickly and neatly. 
Every drawing should have a title, and poor lettering spoils the effect of the whole 
drawing. A good style of letter to use is that given below. The size is 

determined by four lines one-sixteenth of an inch apart, and the letters slope 75°. 
Draw pencil guide lines for the lettsrs, to insure uniform height. 
The small letters are based on the circle, and a straight line tangent to the circle. 
Letters and figures used for notes and dimensions should be only one-eighth of an 
inch high. Letters should be made free-hand and first outlined in pencil. 

When inking, use a writing pen with very little ink, and do not press on the pen 
enough to spread the points. Avoid shading the letters. Let the result be 

clean cut, well formed, properly spaced lettering. 

HUKI MNnPORFiTU\/WXY7 



tihnH fi fqhiJktmnopqrstuvwxy 



MECHANICAL DRAWING 3 

LINES :- When inking a drawing, the weight of a line is regulated by adjusting the screw 

at the sida of the ruling pen. All lines should be of the weights shown below. 



/ 






6" 



No. 1 is for all Visible Lines of the object represented by the drawing except shade lines. 

No. 2 is for Shade Lines. The rule for conventional shade lines:- Make the lower and 

right-hand lines of surfaces, shade lines, excepting lines dividing adjacent visible surfaces. 

No. 3 is for all lines representing Invisible Lines of the object. 

No. 4 is for Dimension Lines, to be made with RED ink. Arrow-heads and Figures should 

always be made with BLACK ink. 

No. 5 is for Center Lines. 



MECHANICAL DRAWING 



PROPORTIONS OF KEYS 

When d = diameter of shaft in inches 
b = breadth of key = \d 
t = thickness of key = f 6 



EFFECTIVE DIAMETER 

of a bolt with U. S. S. Thread = dia. of bolt — I.SOpL 

of a bolt with Sharp V Thread ■=^ aia. of bolt — 1.7 3 2 pi. 



THREADS PER INCH 

Diameter ^ f \" 
No threads 20 16 12 



3l" 
8 



3." 
4 



8 



// 10 9 



1" 
8 



1L" 
'8 



IS." 
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DECIMAL EQUIVALENTS 



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MECHANICAL DRAWING 



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1. Rectangular Prism. 
Make a working drawing showing three views 
of a prism 6\'' long, 3\" wide, and 2" thick. 
Hole through the center of prism is 4^ X 1\"- 
Fig. 1 is a perspective sketch or picture of the 
prism. Figures 2, 3, 4, show in order, the 
top, front, and side views, each in its proper 
position with the other two views. 
These three views, carefully dimensioned, com- 
plete the working drawing. 



2. Grooved Block. 
Make a complete working drawing of a block 
shown by sketch, which is 6\" long, 3\" wide, 
2^' thick 



Grooves are 1^" X ¥' «^<^ ¥ 



from long edges of block. 



MECHANICAL DRAWING 



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3. Hexagonal Prism. 

Make a working drawing showing three views 
of a hexagonal prism 6^ long, and 2-/ across 
parallel sides. 

4. Triangular Prism. 

Make a comphte working drawing of a hollow 
prism which is 6^" long. The ends are 

equilateral triangles with sides 3" long, 
The sides of the prism are Y thick. 

5. Cube, 

Make a working drawing of two views and de- 
velop the surface of a cube with faces 2" X 2' 
Fig. 1 is the sketch, Fig. 2 is the working 
drawing, and Fig 3 is the developed surface. 

6. Square Pyramid. 

Make a working drawing and develop the sur- 
face of the square pyramid shown by sketch. 



MECHANICAL DRAWING 



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£x.8.- 




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— Pt/rom/c/ irCo/,e - 

£x.3 - 




— Crass lap Jo/'nT-\ 

£a.//- 

—A/forT/x o/!c/ Te/fon Joint- 




7. Hexagonal Pyramid. 

Make a working drawing and develop the sur- 
face of a pyramid with hexagonal base, 2f 
across parallel sides, altitude 5". 

8. Cone, 

Make cT working drawing and develop the sur- 
face of a cone with base 2^", altitude 5" 

Make working drawings showing three views 
of each of the joints. 

9. End Lap Joint. 

Each piece is 4|" long, /f " wide, lY thick 

10. Cross Lap Joint. 

Each piece is 5\" long, /f " wide, iy thick. 
Lap is ^" from end of each piece. 

11. Mortise aad Tenon Joint. 

One piece,5Y X H" X IV' with mortise /f " 
X I". Tenon piece, 4^ X H" X H". 



MECHANICAL DRAWING 



8 



-£x.fZ— 




12. Link. 

Make working drawing (front and top views) of 
a link 7" between centers ; each end is 2j"dia. 
2y'liigh; hole, 1^'dia.; bar,1fdia.; fillet, ^"rad. 



-£x. J3 




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13. Bronze Bush for Bearings 
Make three views, with dimensions, of a bush 
5" long, 2^ high, 3^ wide; groove, 2" X i'V 
dia. of bearing, 2^. 



14. Angh Iron. 

Make working drawing ( front and side views ) 
of angle iron with base 4\" X 4\" X ¥> ""^ 
upright 4j" X 6^" X ¥■ Brace is ^" thick, 
extends from top edge of bass to within iy of 
top of upright. Fillets, I" radius. 



MECHANICAL DRAWING 



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15. Cone Pulley 
Sketch shows a half section of a three step 
cone pulley. Make drawing to scale full size. 




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16. 8" Pipe "T" 
In addition to the two views shown in sketch, 
make a top view. The drawing should be 
made to scale \" = T\ 



MECHANICAL DRAWING 




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MECHANICAL DRAWING 



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of inlBf^ecT/on of surfaces. 



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MECHANICAL DRAWING 



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- Deue/opecl surfoc:, 



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MECHANICAL DRAWING 



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MECHANICAL DRAWING 



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MECHANICAL DRAWING 



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—7b /a y out ,^pc/rf- cot/'er — \. 
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MECHANICAL DRAWING 



16 



Angle Iron 



Make drawing io scale full size 







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MECHANICAL DRAWING 



17 



Ratchet Wheel 
24 teeth |" deep. See Formulae for Keys for size of keyway. 

Make drawing to scale full size Section on line a-b 




MECHANICAL DRAWING 



18 



Governor Pulley 



Make drawing to scale full size 




MECHANICAL DRAWING 



19 



Piston Rod Gland and Bushing 
Make drawing io scale full size Section on line a-b 



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MECHANICAL DRAWING 



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- Site role Head - 
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MECHANICAL DRAWING 



21 



MICCHAXICAL DRAW! XG. 

Mechanical Drawing is the art of making draw- 
ings capable of representing mechanical and architec- 
tural structures as a whole and in detail so clearly and 
completely that skilled workmen can make these struc- 
tures exactly as they are intended to be, without any 
further directions than those contained in the draw- 
ings themselves. 

Such drawings made expressly for the workmen 
are called "working drawings." Evidently these draw- 
ings, to meet all requirements, must express easily and 
perfectly all facts in regard to position, form and iiiag- 
iiitude of objects represented. In other words, they 
must be capable of expressing the geometry of all me- 
chanical figures — solid as well as plane — for geometry 
is defined as "that branch of mathematics which treats 
of position, form and magnitude." They must repre- 
sent these solid figures in space, yet the drawing must 
all be in one plane — that of the paper. 

It is evident, then, that the art of -Mechanical Draw- 
ing must have as its foundation an exact mathematical 
science. This is the science of "Projection." Draw- 
ings made in accordance with the methods of Projec- 
tion Drawing meet all requirements completely. 



pROjECTiON Drawing is the science and art of pro- 
ducing drawings which shall represent completely all 
facts of position, form and magnitude of all geometri- 
cal quantities in space. The methods employed in Pro- 
jection Drawing are those of "Orthographic Projec- 
tion" which is the basis of the science of Descriptive 
Geometrv. 



XOTF.S ()X PROJECTIOX. 

ff from a poiv.t in space a straight line is draiK'n to 
a plane, the point in which the line meets the plane is a 
projection of the point in space. The line itself is a 
projecting line. The plane is a plane of projection. 

( )RTHoGR.\i'[iic Pro.h-xtion. In orthographic pro- 
jection (a) a plane of projection is either a vertical 
or a horizorital plane. (The planes ol projection are 
assumed to be transparent.) 

(b) Ever}- projecting line is perj^endicular to the 
corresponding plane of projection; hence, projection 
lines are either vertical or horizontal lines. 

(c) The projection of a point on the vertical plane 



MECHANICAL DRAWING 



22 



of projection is called its vertical projection ; its hori- 
zontal projection is on the horizontal plane of projec- 
tion — hence, horizontal projecting lines are used to 
find vertical projections, and vertical projection lines 
to find horizontal projections. 

(d) A projection of a line may be found from the 
corresponding projection of the limiting points. A 
projection of a surface may be found from the cor- 
responding projections of its limiting lines. A projec- 
tion of a solid may be found from the corresponding 
projection of its lim.iting surface. 

(e) In mechanical drawing, orthographic projec- 
tion is used for the delineation of both the horizontal 
and the vertical projections of material objects upon 
t-ii'o imaginary co-ordinate planes. 

Angles of Projection. The two co-ordinate planes 
of projection intersect at right angles and there form 



four right diedral angles. 



Denoting 



the horizontal 



plane by H and the vertical plane by V, a point, line, 
surface, or solid is said to lie in the first angle when 
it is above H and in front of V ; second angle when it 
is above H and behind V ; third angle when it is below 
H and behind V ; fonrth angle when it. is below H and 
m front of V. 



The third angle is the one commonly used by drafts- 
men for zi'orking drawings, as it affords a more con- 
venient arrangement of views (projections) and is 
more in accord with modern practice. The funda- 
mental principles of drawing are practically the same 
— no matter in which angle the object may be located, 
and a draftsman should be able to draw in all four. 
However, for the present we shall only use the third 
angle of projection. 

Views. Ihe projections of an object on H and V 
are called, respectively, its Horizontal Projection and 
Vertical Projection or Plan and Elevation, or Top 
View and Front Vieiv. Of these three pairs of terms 
Top View and Front View are to be preferred. They 
i re not only more definite, but they are more con- 
sistent with Bottom View, End Viezu, Side Viczv, or 
Rear View — terms commonly used in working draw- 
ings when the corresponding views of the object are 
shown. 

The projection lines which determine anv one view 
of an object are all parallel. These lines correspond 
to lines of sight, but lines of sight are never parallel — 
hence a projection is never a true picture. The term 
view must therefore be used onlv in the sense of a 



MECHANICAL DRAWING 



23 



projection. The line in which IT and V intersect is 
called the ground line. 

The Drawing, (a) To represent the planes of 
projection, a horizontal line is drawn to represent the 
ground line. That portion of the paper above or behind 
this line represents one plane of projection; that por- 
tion of the paper below or in front of this line repre- 
sents the other plane of projection. H is behind 
and V is below the ground line when the third angle 
of projection is used. 

(b) The relative positions of the different views 
or projections, with respect to the ground line and to 
each other, are the same as would result if one of the 
planes of projection were revolved about the ground 
line imtil H and V were both in the same plane. 

(c) In orthographic projection any point in the 
third angle has its top view (horizontal projection) be- 
hind, and its front view (vertical projection) below the 
ground line. 

(d) Orthographic projection thus requires of the 
imagination two distinct processes : ( i ) To con- 
ceive each viezv on ike corresponding plane of projec- 
tion. 

(2) To determine the position, of the different 



inezus zvith rcst>ecl to the ground line and to each other 
when the planes of projection have been brought into 
one plane. 

A Point in Space, (a) Every point has two 
views (one on H, the other on V) by which its posi- 
tion in space is determined. 

(b) A point and its two views lie in the same plane 
perpendicular to both H and Y — i. e., a plane passed 
through the two projecting lines. 

(c) The Top Viezv of a point is as far behind the 
ground line as the point itself is behind V. The Front 
Viezv of a point is as far below the ground line as 
the point itself is below H. 

(d) When a point lies in either H or \' one of its 
\ lews coincides with the point itself ; the other view 
will lie in the ground line. 

(e) A point in space can be represented bv its two 
views, neither of which is the point itself. 

(f) The two views of a point always lie in the 
same straight line at right angles to the ground line. 

A Line in Space. Straight lines perpendicular to 
H and J'. 

(a) A line perpendicular to either pkme of projec- 
tion has for its view on that plane simply a point. 



MECHANICAL DRAWING 

(b) A line perpendicular to either plane of projec- 
tion has for its view on the other plane a straight line 
perpendicular to the eround line, and equal in length 
to the line of which it is the projection. 

Straight li)ies parallel to one plane of projection, but 
(./ an angle with the other. 

(a) When a line is parallel to either plane of pro- 
jection its view on that plane represents the true length 
of the line ; and the angle which this view makes with 
the ground line is equal to the angle which the line 
in space makes with the plane to which it is not par- 
allel. 

(b) A line parallel to eitlier plane of projection 
iias for its view on the other plane a line parallel to 
the ground line. 

(c) When a line is not parallel to a plane of pro- 
jection its view on that plane is always shorter than 
the true length of the line. 

Lines parallel to both H and V, and lines parallel 
to neither H nor V. 

(a) A line parallel to both H and V has for its two 
views lines parallel to the ground line, both of which 
are equal in length to the line itself. 

(b) If a line is parallel to neither plane of projec- 



24 



tion, both views are shorter than the line itself. The 
angles which the line makes with the planes of pro- 
jection are not represented in their true size by the 
angles which the views make with the ground line. 



MECHANICAL DRAWING 



25 



PROBLEMS IN PROJECTION. 

1. Represent 

(a) A line l^" long^, perpendicular to H, 

V from V, top end f below H. 

(b) A line li" long-, perpendicular to Y, 

^" from H, nearest end V from V. 

(c) A line if" long, parallel to V, slanting 

downward to the right, at 60° with 
H, I" from V, top end |" below H, 

(d) A line if long, parallel to H, slanting 

back 60° with V, toward the right, 
I ' from H, and nearest end V from 
V. 

2. Make the apparent projection in V of a line 2" 
long, slanting downward to the left at 45° with H, 
and backwards 45° with V. Its top end is -|' from 
both H and V. 

3. A line appears i^" long at an angle of 45 "^ 
with both H and V. Its top end is ^" below H and 1 1 ' 
fiom V. The line slants downward, forward, and to 
the right. Find its true length, and the angle it makt^s 
with H. 

4. A line slanting downward, forward, and to the 
right, appears to be 2" long at 60' with H. Its top 



view makes an angle of 45° with Y. The top end is 
-i" below H and iV behind V. Find the true lengili 
of the line and the actual angles the line makes witli 
both H and V. 

5. A line appears slanting downward, backward, 
and to the left. The H projection is at 30° with V 
and 2-1" long. The V projection appears at 30° with 
H, and the top end of the line is -J" from both H and 
V. Find the true length of the line and the angle it 
makes with V. 

6. The profile projection of a line shows it placed 
at 30° with V and 60° with H. The top end of the 
line is -^- below H and i" behind V. The line is i-V 
long and slants toward V. Make the horizontal and 
vertical projections of the line. The line is t" be- 
hind the profile plane. 

7. Draw top and front views 

(a) Of a card i^" square perpendicular to 

li, parallel to and 4' behind \'. Its 
top edge is j below H. 

(b) Of the same card turned back to the 

right at 45 ' with \'. 

(c) Of the same card when, besides being- 

turned back at 45'' to V, the edges 



MECHANICAL DRAWING 



26 



which were parallel to H make an 
angle of 45° to H. The card is 
tipped over toward the right. 

8. Draw top and front views 

(a) Of an equilateral triangular card, sides 

1 1" long, when it is parallel with 11 
and its front edge parallel with V. 
The front edge is i" behind V and 1" 
below H. 

(b) Of the same card when its front edge 

slants down to the right at 30° with 
H. 

(c) Of the same card when its front edge, 

besides slanting downward to the 
right at 30° with H, is turned back 
toward the right at 45° with V. 

9. Draw the front and top views 

(a) Of a cube with faces i" square, its top 

face parallel to and 5" below H, its 
front face parallel to and -J' behind 

(b) Of the same cube when its front face 

is parallel with V and its top face is 
at 30° with H. the cube tipped over 



toward the right, 
(c) Of the same cube when, besides having 
its top face at 30° with H, has its 
front face turned back toward the 
left at 30° with V. 
10. Draw the top and front views 

(a) Of an equilateral triangular prism, 

with the sides of the base of the 
prism i|-" long, the prism being 'f'' 
thick. The triangular faces are 
parallel to V, the front face V 
behind V, and the lower rectangular 
face is parallel to, and if" from H. 

(b) Of the same prism when it is tipped 

over toward the right so that its low- 
er rectangular face is at 45° with 
H, the front face parallel to V. 

(c) Of the same prism when its lower rec- 

t-ingular face is at 45° with H, and 
its front face is turned backward to- 
ward the right at 45° with V. 
II. (a) The front face of a rectangular block is 
4I" long, if" wide, and is placed 
parallel to and i" from V. The tO]) 



MECHANICAL DRAWING 



27 



face is at 30° with H, and tipped up 
to the right. The top view shows 
that the block is i^" thick, 
(b) Make the top and front views of the 
same block when its lower face is- at 
30° with H and its front face is 
turned at 15° toward the right from 
V. 

12. (a) Make the top and front views of a square 

prism 3^"x3^"xi:J:", with the square 
faces parallel to H, and its front rec- 
tangular face at 15° with V, turned 
to the left. There is a hole 2 ' square 
through the block. The nearest 
corner is \'' behind V and the top 
face 2\" below H. 
(b) The same block when besides being- 
turned to the left at 15° with V, is 
tipped up at the right so that the 
square faces make an angle of 30' 
with H. 

13. (a) A pyramid 3V' high and base 2" 

square is placed with the base 4" be- 
low and parallel to H, and the sides 



of the base at 45° with V. The near- 
est corner is i" behind V. Make 
top and front views. 

(b) Same pyramid with the base at ^o" 

with V and tipped over toward the 
right at 30° with H. 

(c) Same pyramid when besides having its 

base at 30° with H, its axis turned 
away toward the right at 45 ° with \' . 
14. (a) Make the top and front views of an 

equilateral triangular pyramid whose 
sides at the base are 2J-'' long, the 
pyramid being 3^' high. The base 
is 4" below and parallel to H. The 
left side of base makes an angle of 
75° with V. 

(b) Same pyramid with the left side of 

base at 75° with V[, and the base at 
30° with H, pyramid tipped over 
toward the right. 

(c) Same pyramid with base at 30° with H 

and the left side brought forward, 
making an angle of 30° with V. 



MECHANICAL DRAWING 



28 



15. Make the apparent V - projection of an L- 17. Make the apparent V pi^ojection of two inter- 
shaped block, when the lower face of the block is at secting square prisms, when the lowest face is at 30° 
30° with H, and the front face is at 30° with V. vvithrH and the front edges are at 15° with V. 

\ ce/fA^r //he o//iyOrojecT/on ,. g gf^ 

>r-T— 1 r-i 1 , / i, cCl"^"''' 




rtm 



>_ 
wi 




T:'?e /'/r/Srsec///?^ omm s 
a^e eac/f ■i'"x /"j(/' 



16. Make the apparent V projection of an H- 18. Make the apparent V projection of a cylinder, 
shaped block, when the lower faces of the block are at when its axis is at 45° with H and 15° with V. 
15° with H and the front face is at 15° with V. 




•^ / 


^-s 


V'" -'-/I 


llN 




'^\ 








■N- 




1 






^ 


v„.„ 


t.^x? 






V 


4 

/ / / 

/ / /Y 


7 





wy 



flX/? 



oLcHliS^'\ 



C^//.'ye>' ef^/s£'ci'/?/A'3j /mc, ' 



MECHANICAL DRAWING 



29 



WORKING DRAWINGS. 

WoRKiXG Drawings are drawings showing machine 
or architectural construction as a whole or in detail so 
clearly and completely tnat a workman can make the 
desired construction exactly as it is intended to be with- 
out any other directions than those contained in the 
drawings themselves. The student or draftsman, then, 
should keep in mind the following general rules when 
making working drawings : 

A working drawing may be divided into three parts : 
( I ) The outline drawing showing the shape 
of the object; (2) the dimensions giving the 
size of every part; (3) the lettering — i. c, 
printed explanations and directions. In worr. - 
ing drawings the object is represented by two 
or more views, each of which is drawn according to 
the principles of projection. Hence, these views art 
really projections- — rot figures; and as many views 
must be shown as may be necessary to completely 
represent the object. In the arrangement of views the 
top view is drawn above the front view, the bottom 
view below the front view, and the end view nearest the 
end it represents, etc. When a section view is drawn, 
ihe point at which the section is taken is indicated on 



one or the other views. The usual way is to draw a 
f-ace of the cutting plane, lettering it and marking the 
section view to correspond — as, for example, section 
at A— B. 

The Dr.\wing shows the shape of the object. It 
may be made to any convenient scale — as full size, 
half size, quarter size, etc. Shop units are feet and 
inches and parts of an inch. The fractional scale of 
8ths, i6ths, and 32ds is generally used, although some- 
times the decimal scale is preferred where drawings of 
machinery are made. Drawings are first made in pen- 
cil. If a number of copies a;e required, instead of ink- 
ing the drawing on the original sheet a tracing is made 
and blue prints taken. A drawing which represents the 
object complete with, each part in its proper place is 
called an Assembled DRAV\•i^'G. A Detailed Draw- 
ing should have each part by itself. 

When drawings are to be made on sm.all sheets draw 
one detail on each sheet, using largest scale possible. 
Draw all small details full size. When drawings are to 
be made on large sheets, distribu'.e details on sheets so 
as to have all details of ore part of the object on the 
same sheet and in a group apart from similar groups 
of other details. If possible, draw the front view of 



MECHANICAL DRAWING 



30 



each detail in the same position, vertically or horizon- 
tally, that it appears in the assembled object. If desir- 
able, details may be distributed so that the castings and 
forgings will be upon separate sheets. If possible, 
make all drawings on one sheet to the same scale. 

After the size of the sheet has been decided upon, 
make a rough sketch composed of rectangles showing 
the approximate location of views and distances be- 
tween them, allowing a space of at least i-J ' x 3" in tlie 
lower right hand corner for the main title. Start draw- 
ing bv laying out all center lines of views, and mark 
off their location on sheet before drawing outlines of 
views ; place dimensions on views before section lin- 
ing. Section lines should not be drawn parallel to any 
line of the drawing, if possible. Where a part of the 
detail is to be finished a small "f" is printed on the 
line representing the surface to be finished, with the 
cross bar of the "f" on the line. Where a special finish 
is desired, a note stating the character of the finish is 
printed adjacent to the surface to be finished. Where 
a detail is to be finished all over, it is stated thus,— '"f 
all over." Special notes which would be of value to 
the workman and save extra drawing should be freely 
used. 



Each detail should have a sub-title stating its name, 
numiber of pieces wanted, and kind of material of 
which it is to be made. Pattern numbers should be in- 
dicated on drawings and castings. Each detail should 
be numbered, as well as the drawing, and these num- 
bers should appear on the assembly drawing. The 
main title should state briefly the name of detail or 
details, the name of the object of which the detail is 
a part, the scale or scales, the date, and draftsman's 
name or initials. 

The drawings of an object should contain sufficient 
views in section to completely show its construction ; 
and each detail should be fully dimensioned to show 
its size and relation to other parts of the object. 

The front viczu or clezatioii is usually that view of 
the object which, if taken alone, would convey the best 
idea of its propcrtior.s and construction. The top 
view or plan is the view looking down on the object; 
and end viezvs or side ziczvs may be used with or in 
place of the top view. Bottom and oblique z'iezi's arc 
used only where the usual views do not clearly show 
the entire construction. 



MECHANICAL DRAWING 31 

Sections. Sectional views are made to show the able. The dimensions on a drawing are those of the 

shape of certain parts of the object which can not be object represented, no matter what the scale may be. 

well designated in the different views. Section lintrs It is better to leave a space in the middle of each di- 

should usually be made at an angle of 45" to the i niension line for the dimension than to write figur-'S 

square, and about 1-16 of an inch apart. Sections of above or below the line. If the dimension line is so 

the same part should have the section lines running in short that a dimension can not be given on it, the lat- 

the same direction. Section lines should run in oppo- ter is placed to one side, and an arrow indicates where 

site directions when the section is shown through two it belongs. Any dim.cnsion less than one foot is given 

separate or adjacent parts. in inches — not in decimal parts of a foot. Anything 

less than an inch is given by the nearest vulgar frac- 

DiMENSioNS. The size of every part of an object is tion whose denominator is 64, 32, 16, 8, 4, or 2. Any 
given by the dimension lines and figures. Dimension other fraction should be given in decimal form. As 
LINES show exactly from what poiiit to what point the a rule the line between the numerator and denominator 
measurement is to be made. Such lines should be dis- of a fraction should not be oblique. Feet and Inches 
tinguished from the regular lines of the drawing. They are indicated thus — 6' 3". If a dimension is in even 
are sometimes fine, broken lines, very fine black lines, feet, or in feet and a fraction of an inch, o" should be 
or red lines. Red lines on a tracing print more faintly noted, like this — 2' o', or 11' o -J". Long dimensions 
on blue process paper than do the black lines, and this are put on first, and those are subdivided and re-sub- 
has the effect of making the drawing stand out with divided as may be necessary. Care is necessary to 
the dimension lines in the background. make the subdivision foot up the longer length. "Over- 
all dimensions'' are of considerable importance to save 
Dimension Figures and the Arrowheads at the the workman the trouble of footing up or adding to- 
ends of the dimension line, however, should akvays be gether a number of smaller lengths. Dimension lines 
blue:;. FiojRES should be plain, heavy, and unmistak- should not cross each other when it can be avoided. 



MECHANICAL DRAWING 



32 



and should stop at exactly the right place. A drawing 
is usually made to scale ; but if scale and dimensions 
as given do not agree, the dimensions are always as- 
sumed to be correct and govern the men in the shop. 
In some shops workmen are not allowed to scale draw- 
ings, but must use only the written dimensions. The 
workmen should have all the questions which he may 
need to ask answered on the drawing itself; therefore 
the notes are an important part of the working draw- 
ing. 

Dimensions must be just sufficient in number to re- 
move any doubt as to the size of any part and its re- 
lation to other parts or to the whole construction, and 
they should not be repeated in other views. Dimen- 
sions should be placed upon the drawing so as not to 
interfere with the clearness of the drawing or to be 
confused with other dimensions. The particular space 
dimensioned should be so chosen as to avoid the ne- 
cessity of additions or subtractions by the workman in 
executing the work. 

Dimension Lines. For linear measurements the 
lines must be perpendicular to the parallel lines or sur- 



faces between which the dimension is taken. For aneij- 
lar measurements the lines must be arcs described from 
the vertex of the angle. For diameters of circles the line 
must be a diameter other than that which would coin- 
cide with the vertical or horizontal center line of the 
circle. The line may also be a line drawn parallel to a 
diameter of a circle and perpendicular to a tangent 
drawn at the extremities of the diameter used. For 
dimersioning ridii of arcs the line is to be drawn from 
the center of the arc. For measurements of i" or less 
the line is to be drawn in two parts, each part being 
outside of the space dimension. For adjacent meas- 
urement lines in the same direction the lines are to 
be as one continuous line. For a series of dimensions 
in the same direction of which some are the sum total 
of the others, Hnes are to be drawn in the order of 
their magnitude, the longest being drawn farthest out- 
side. Dimension lines should not be closer than i" 
to line of object or to other dimension lines, drawn 
parallel to them. Termination lines should not touch 
any line of the object, if possible, and must be perpen- 
dicular to the dimension line. They must be perpen- 
dicular to the line of the object being dimensioned, and 
should extend to the dimension line. 



MECHANICAL DRAWING 33 

Suggestions. If one view shows a larger portion 
of the object in its true shape and size than any other 
view, start that view first. Estimate the space each 
view will occupy, and draw center lines, allowing 
space enough between the views for dimensions. Build 
up each view about its center lines. Project views 
from one view to another to save work with the scale. 
It is often impossible to complete one view at a time, 
and in many cases it is necessary to carry along two 
or more views simultaneously, drawing the main out- 
ii:;es first — details last. Be sure important measure- 
ments to center lines, etc., are correct before putting in 
dimensions or smaller details depending upon them. 
If a dimension is altered, change all dimensions relat- 
ing to or depending upon it to correspond. 

Order of Inking. Arcs of circles, irregular curves, 
straight lines, center lines, dimension lines, dimensions, 
section lines, notes, title, and border lines. 



/ 



MECHANICAL DRAWING 



34 




>- y i L 



e ■- /} -> 



~ h ~.t>. 



BRONZE SEAT for BEARINGS 



The drawing shows a bronza seat designed for pillow-block or pedestal bearings. 

The following proportions may be used, based on the diameter of the shaft — "d" 
a=. 1\d b= .1d-\-\" c= i^ + r e= \d-^ 

f= .Id g= id h= id i = 

j= -Ld-\-f k= iy m= i" n = 



8 
8 



MECHANICAL DRAWING 



35 




FLAT-LINK CHAIN 

Flat-link chains are used for driving machinery where heavy resistances are to be overcome, 
as in cranes and dredging machines. When the chain merely supports a load, the following 
proportions may be used, based on the diameter of the pin — "d" 

b^. nd c= 2y e= id r = b 



a 



iy 



d + .05" / =z 4to8d s = 



MECHANICAL DRAWING 36 

SCREW THREAD FORf/ML/E 

The SCREW is a cylinder, upon whicfi has been formed a he/ica/ projection 
or thread. The screw fits into a hollow corresponding form called the NUT. 

The PITCH of a screw, is the distance from the center of one thread, to the 
center of the next thread, measured parallel with the axis of screw. 

The LEAD of a screv/, is the distance its nut would travel along the axis in 
one turn of the screw. The Nominal Diameter is that of the cylinder upon which the 
thread is cut The Effective Diameter is the diameter at the bottom of the threads. 

For the U. S. Standard Thread, when d = nominal diameter of bolt, 

p = pitch of thread, = 0.24y/fd-{- 0.625) — 0.175 

n = number of threads per inch, = 1 -^ p 

X = depth of thread, = 0.75 X p(sin.60°) = 0.65p 

jr, = total depth of V, = pfsin.60°J = 0.866p 

e = effective diameter of bolt, = d — 2x 

t = thickness of nut, = diameter of bolt. 

h = thickness of bolt head, = 0.75 X d ^ 0.0625 

f ■= distance between parallel sides of head and nut, = 1.5 X d -\- 0.125 

f^ = distance across corners of hexagonal nut, = 1.155 X f 

/j = distance across corners of square nut = y/2f^ 



MECHANICAL DRAWING 



37 



- Sharp // T/)read - 



-"-^O^ 




Sere w 77? rea ds tj-^ ^ , , . -y. ^--^^ 
^^ U.6.Stancfard Thread -% \ 



Square Thread — 







/-_ 




,-/?//&/« i 




— Moc//f/'ed <Souore Th^eoc/ - 




- WhitworMEngZ/sh SfiJ) T/7 read y 




MECHANICAL DRAWING 



38 



-7??e /ie//x- 



1 


1 


^ 


/^•^-^ 


f^ 


P 


f 






1 


\ 


\ 


4 


\ 


/ 


/ 


7 




^ 


^ 


3r 


^ 


s 


«; 






4 








^ 




















^ 




7 

r 

9 












N 


























^'i 










? 






// 
/i 






,-•'/ 


i? 






't 


'/ 






^ -.J-' 














^•T^ 











— /{pp//coT/on of /^e /Yef/'x- 

6/7orp y Tf7/^eoc/ :-3."joi. • d^aore T/ifeacf f /J"pi.— 



Oroiv S 



TJtreaefs 



Drott^ S 7 'hz-eoe/s . 




~2^ 



fl 



MECHANICAL DRAWING 



39 




CyOni/enTiona/ Threads 



1 



'lariol''-^/}/ /ef/^honcl - - 



■^10^ 



DrOi^ //7 /^e ^fe£)r?.'! i 



— //- 



■^- 



J 



o^l- 



-^ /■ -1^ 



1 


\ 
^0 




\ 





\ 


(ZirOtAy /'rj ^e /^"reor/s \ 


in 




'7' 


^. 


'a 







■A^od/l/ecjAquoi ^iegd fp/riohrhnnd — 




IV 



JDr^t^ /'/7 ^e 7^re^ef > 



7- - 
^2 






MECHANICAL DRAWING 

To draw a BOLT wiih HEXAGONAL HEAD and NUT 



40 



First make calculaiions (using the Screw Thread Formu/ce) for parts f, t, h, and 
p, when d = dia. of bolt. The conventional method used to represent the chamfer on the 
head and nut is shown in the drawing. 

In Fig. 2, with center at 2, and r ad. 2-1 . draw arc 1-3 ; with centers at 1 and 3, 
draw arcs 2-8 and 2-7 ; with 7 and 8 as centers, draw lines tangent to line 1-3. 

In Fig. 4, with center on the center line of bolt and rad. = 3-A, (w) draw an arc 
tangent to line 3-4 ; bisect lines 2-3 and 4-5 in Fig. 3 at 9 and 10, and draw lines from 
these points obtaining 9 and 10 in Fig. 4. With 9 and 10 as centers, draw arcs tangent 
to line 2-5, and complete the chamfer by drawing lines at 45", tangent to these arcs. 

d = .1^... I =z ..<c>.'.! 




MECHANICAL DRAWING 



41 




-Ta p Bolt 



rfi 



MECHANICAL DRAWtNC 



42 




Daub/e 1/ 3r..- 



ConyenfJono/ Threads. — 



vT- 



'3i ^e/a^e Jfy o^/?// Deam- osa 





Me >Screw nreod Formt//ce - 



40^ 



MECHANICAL DRAWING 



43 



STUFFING-BOX 

The stuffing-box shown by the drawing /s generally used for small work, such as vahe 
spfrdUs, tic. The outside of the siuffrg-tcx (B) is threaded to receive a hexagonal 

nut (N) that fits over the gland(G). As the nut is screwed down, the gland is pressed 

down and compresses the packing. Ths proportions given are for rods up to 1\" dia. 



I^t d 




a 


2.5d + .5" 


b — 


1.5d -1- .125" 


c 


3d-[- .25' 


e 


3.5d + .625" 


f — 


d + .125" 


y — 


.75d 


h — 


1.5o/\- .25" 


i — 


.25J -i- .0625" 


k — 


.5d 


m 


2d + .125" 


n 


e .5d 





2.5d 


r 


.6d 


s 


.75d 


t — 


..Id 


U ■ 


h 




Make the number of 
threads per inch the same as 
for a bolt whose diameter is 
equal to the diameter of the 
rod. 



In addition to the 
two views given, make a third 
view showing ths outside of 
the stuffing-box. 



MECHANICAL DRAWING 



44 



Sketches for 1\" Glob- Valve 




MECHANICAL DRAWING 



45 



SHAFT COUPLING 



The drawing shows a flange coupling, made by keying cast-iron flanges to the 
ends of the shafts. The following proportions, based on the diameter of the shaft, 

( d ) may be used in drawing the coupling for shafts from 1" to 3^ in diameter. 



Leid — 




a 


2.35d 


b — 


1.6d 


c 


2d 


e 


c .25" 


f — 


.875d 


9 — 


1.25d 


h — 


.375d 


1 


.25d 


J — 


.375d 


k — 


J25d 




MECHANICAL DRAWING 



46 




ENGINE CRANK 
The drawing shows a crank designed for slow speed engines. When D = dia. of the 
engine cylinder, and T = the travel of the piston, the following proportions may be used. 
0= d b= 1.75d c = .05d -\- .06" d r= .50 

e= i" /= .37 5g h= 1.35p i— 1.125d 

l=z,26D-j-^" m= d — \" n= p — Y o= n -{-"\ 

p= .280 t= .5T g is found by drawing lines tangent to i and b 



MECHANICAL DRAWING 



47 



PIVOT or FOOT-STEP BEARING 

The drawing shows a bearing designed to support the ends of vertical 
shafts. The end of the shaft rotates on the central disk, which may be made of steel, 
brass, or bronze. The brass bush prevents the shaft from moving side- ways. 

The following proportions, based on the diameter of the shaft, ( d ) may 



be used in drawing the bearing. 

? 



Letd = 




a = 4d 

b = 1.5d 

c = 0.25d 4- 0.375' 



e — 




1.25d 


f — 


0.2d 4- 


0.125" 


y — 




1.7 5 d 


h — 




1.4d 


1 




07d 


• 

J — 




0.4d 


k — 




0.3d 


/ — 




0.1 5 d 


m 




1.5d 


n 


0.2d-\- 


0.25" 





!f\ 


0.15d 



MECHANICAL DRAWING 



48 




STUFFING BOX 

The following proportions may ba used for stuffing boxes of this style for rods up to 3^' dia. 

d = dia. of rod 

9 —e -\-\d k = i — g 

h =2d-{-\" / = 2y -\- /f 

/ = l^d -I- /" m= iy + 1^ q = n 



a 
b 



hd + 1" 



n 



.Id -f I" 



8 



= \d-^Y 

p = i±d-^r 



MECHANICAL DRAWING 



49 



Too/ fbs-f- a/t</ Corr/a^ff 
—/6//7. LaZ/ie — 

— /^.•J./'/ia/ofr. — 

rfi 




f./e/>i. 




Make data's! drawings of each part. 



t 



MECHANICAL DRAWING 50 

PEDESTAL BOX or BEARING 

The following proportions may be used for pedestal boxes of this style for shafts up to 2{" d/a. 



d — 


diameter of shaft. 




a 


2id 


n 


¥ 


h—. 


iy 





^"(constant) 


c 


d 


P — 


1\d 


e 


^d 


9 — 


Hd 


f — 


id 


r 


¥ 


9 — 


Hd 


s 


{"(constant) 


h — 


2\d 


t — 


¥ 


i 


y 


u 


i¥ 


a 

J — 


¥ 


V 


¥ 


k — 


id + / 


w 


H' 


1 — 


¥ 


X 


i'' 


m 


id + V 


y — 


• 

/ 




MECHANICAL DRAWING 



51 







MECHANICAL DRAWING 



52 






a-. 




MECHANICAL DRAWING 



53 



Jl^sto^e^ /<yr (S^^^ CM^ry^ pPl 




KWI-- 



m 



tr 



MECHANICAL DRAWING 



54 



Efi 







MECHANICAL DRAWING 



55 




Sketch of Faceplate for 9" Speed Lathe 



Thread 1{' dia. 12 pi. 



V.V 



MECHANICAL DRAWING 



56 




Head for 9" Speed Lathe 



Make detail drawings of each part. 



MECHANICAL DRAWING 



57 



-The /iexaqona/ A/i/t^ 




MECHANICAL DRAWING 



58 




MECHANICAL DRAWING 



59 



■Menod for cframm penTnga. 




- F/ni'sh ftoffT i/Zew <s^oivmo ySec^nn . 



MECHANICAL DRAWING 



60 



- Coupling for 6 hafts upto Ijcffa . 



— ProporT'/ o/ys — 




' 



MECHANICAL DRAWING 61 

ISOMETRIC DRAWING 

Isometric Drawing is based on the following fundamental principles :- 

1. There are three lines called "isometric axes," a 30° line to the right, a 30° line 
to the left, at the end of a vertical line. 

2. These isometric axes represent lines that are mutually perpendicular to each other, 
and correspond to the three dimensions, of length, breadth and height. 

3. A mjasuremjnt on tha drawing, can only be laid off parallel to ons of these 
isometric axes. 

4. Vertical lines in the object, are vertical in the drawing. 

5' Parallel lines in the object, are parallel in the drawing. 

6. Lines at right angles in the object, are shown at 60° or 120° to each other in the 
drawing. 



MECHANICAL DRAWING 



62 




-/60/nerr/c Pro/ecPo/r of Col>e 






1 to c 3 



V 






-/someTr/c Dran/m of Hexo(/o/7oJ fy/sm. — 



-Ex.3- 




-£x.^.- 



AfoAe dtauu/ng fo scale. 

— IzW"- 

- Jsomerr/c Org wing of fSfeps - 




-fiSonieWc Dmit'/M^ o/0>cfe or?c/Q///hc/eK — 



/ 



MECHANICAL DRAWING 



63 



-Ek.6- 




— /sometf/c Draiving of Trestfe - 



-^x.6r 




— /So/ne^/c Dram/rg o/Pec/esTa/ Box — 



-f^- 



-£x. W 



& 
C 





1_W7"1-^ 


\ 


TV ' JT 




\ ^-^ ' 


t 


1 ,, r 




/■someTr/c Dram^Q o/Bi^s^/f/C- 




-/S0/ne7f/c Draii^/A7Cf o/'Anp/e /ro/r. — 



1 



MECHANICAL DRAWING 



64 



£JL9z 



—Rotc/?et— 




2^teefff -§-de ep . 

° . -C .1, / 



S^TSr 




V* £ 



— AfaAe IsomeMc Dramn cir 




^ '=^7 ^ ^r, 



MECHANICAL DRAWING 



65 



MOTION, 
(i) A body is moving uniformly when it moves 
over equal spaces in equal successive intervals of 
time. The rate at which it moves is called the veloc- 
ity. 

(2) If the body docs not pass over equal spaces in 
equal successive intervals of time, the motion is said 
to be variable. If velocity increases, it is said to be 
accelerated. If velocity diminishes, it is said to be re- 
tarded. Variable motion may be uniformly accelerated 
or retarded. 

(3) When a body moves forward in the same path 
the motion is continuous. 

(4) A body moving forward and backward alter- 
nately is said to have reciprocating motion. 

(5) A body giving motion to another body, either 
by direct or indirect contact, is called the driver. The 
body receiving the motion is called the follower. 

(6) Rectilinear motion denotes motion in a straight 
line. It can be continuous or reciprocating. 

(7) Rotation denotes motion around a fixed axis. 
This motion may be continuous or reciprocating. If 
the latter, it is said to be oscillating. 

(8) The arrangements used for transmitting mo- 



tion are known by the general term "Mechanism." 

(9) The different wnys by which motion may be 
transmitted are : 

a. Sliding contact — cams, etc. 

b. Rolling contact — gears, etc. 

c. Rolling contact — belts, etc. 

d. Lever connections. 

CAMS. . 

A cam is a device for communicating motion to an- 
other piece by means of the action of its curved edge. 
This crrved edge is usually the irregular face of a 
disc that acts as a driver to a follower in contact 
with it, or else it is a groove cut in a flat or curved 
surface. 

Cams are useful in many forms of machines, as 
through their use complicated movements may be 
made which otherwise would be impossible. They 
have a wide use in many familiir machines — such as 
printing presses, sewing machines, looms, and auto- 
matic machinery of various kinds. The process of 
hying out cams is verv simple, and the general method 
is illustrated in the drawing of the heart shape cam 
shown in Figure 2. This cam is used for converting 



MECHANICAL DRAWING 



66 



circular motion into uniform reciprocating motion. 
The throw of the cam is the distance the follower point 
travels through the whole or part revolution of tb.o 
cam. 

Let it he required to lay out a cam which shall move 
a follower point uniformly along a straight line i i ' 
and return in one revolution of the cam. 

First lay out a diagram of the motion of the fol- 
lower point: let a straight line of indefinite length 
(o — o', Fig. I ) represent one-half of the revolution 
of the cam. At one end erect a line perpendicular to 
the line o — o', and i|" long. Connect the upper end 
of this line with opposite end of the line o — o', then 
divide the line o — o' into any number of equal divis- 
ions, and erect perpendiculars at these divisions. These 
divisions represent successive even intervals of time. 
Drawing lines parallel to oo' from the divisions on the 
lines o — 12, we get the distance the follower point 
will travel in each successive even interval of time. 
To trace the cam curve (Fig. 2) first locate the centor 
of the cam (c) and draw a semi-circle whose radius 
is the distance from the center of the cam to the fol- 
lower point. Divide this semi-circle into the same 
number of equal parts into which the line o — o' was 



divided. Draw radial lines through these points of 
division indefinitely beyond the semi-circle. Then on 
line — 12 lay off the divisions representing the travel 
of the follower point, and draw arcs of circles to rhe 
corresponding radial lines. Drawing a line through 
the points of intersection of arcs and radial lines, we 
get the outline of a curve which will give the desired 
movcmert to the follower point. To complete the 
cam, it will be necessary to draw the opposite side 
of the cam in the same manner. 



MECHANICAL DRAWING 



67 










Co/77. 



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MECHANICAL DRAWING 



68 



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MECHANICAL DRAWING 



69 



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MECHANICAL DRAWING 



70 



Draw the path of motion of point a during the revolution of the crank. 




MECHANtCAL DRAWING 



71 



Draw the path of motion of point a during the revolution of the crank. 




MECHANICAL DRAWING 



72 



(a) When ab = be, with a and b as fixed 
points, find the path of motion, and distancd 
through which d can move each side of line ad. 

(b) If, when ab = be, with a and b as fixed 
points, b and d should b3 conndctzd by a link 
crossing c, what would be the path of motion, 
and distance through which c can move each 
side of line ac. 




MECHANICAL DRAWING 



73 




l^'th ao/fado6ffxedfioinn,p/oTjoamo/e. 



MECHANICAL DRAWING 



74 



GEAR WHEELS. 




if,-*4Jli3J*u»^ xir|iM_jj^ C<////?c/e/-s 

If two cylinders on parallel axes touch each other. 
and we exert power on one cylinder, the adliesion ot 
its surface under pressure to the surface of the other 
will make that turn also. If these cylinders are of 
the same size, each will make the same number of 
turns, but if one be twice as large as the other, the 
smaller will make two turns while the larger makes 
one, and this relative difference in velocity is regu- 
lated by the relative difference in the size of the re- 
spective cylinders. 

This is the primary theory of gearing, and would 
be very useful in mechanics if the one cylinder would 
always turn the other without loss of power occasion.-d 
by slipping. To overcome this, on the periphery ot 
these cylinders cut equi-distant grooves. These 
grooves are called Dedcnda (to take from, to deduct). 



The spaces between these grooves are called Lands. 
Upon these lands add parts. These parts are called 
Addenda (to add, to increase). A land and its ad~ 
d Old inn is called a Tooth. A toothed cylinder or 
wheel is called a Gear. Two or more gears with 
teeth engaging each other are called a Train. A line 
between the centers of two wheels is called the Line of 
Centers. A circle touching the addenda is called the 
Addendum Circle, which represents the extreme cir- 
cumference of the gear wheels, the original circumfer- 
crce of the cylinders without teeth is called the Pitch 
Line or Pit.h Circle, which represents approximately 
Dec/en c/c//?7 rlo/Jcy 




f/g.2 '■P/rc/r C/>c/et^^ic^e/7r/cm 

the center of the tooth from top to bottom. The circle 
exists geometrically in every gear, and. in the studv 
of gear wheels, the problem is to shape the teeth so that 

the pitch circles ivill just touch each other luithout 
slipping. 



I 



MECHANICAL DRAWING 



75 



The groove between two teeth is called a Space. Ln 
cut gears, the width of a space and the thickness of a 
tooth at the pitch circle should be equal. 
Outside Dh/77e^r 




^ P/Tch D/ome/^r 

The distance between the center of one tooth and 
the center of the next tooth, measuring along the pitch 
circle, is the Circular Pitch; that is, the circular pitch 
is equal to one tooth and one space. If the circum- 
ference of the pitch line or circle is divided by the 
number of teeth in the gear, the quotient will be the 
circular pitch. 

The diameter of a gear wheel is always taken at the 
pitch circle, unless otherwise stated. When the teeth 
of gears engage to the proper distance, they are saul 
to be in gear. If two wheels or gears are to be geared 
together, their teeth must be the same pitch. 



Diametral Pitch is the number of teeth in a gear, 
per inch of diameter of pitch circle ; hence, if the num- 
ber of teeth in a gear be divided by the diam.eter of the 
pitch circle, the quotient will be the diametral pitch. 

Diameisr of pUch circle, 

for circular pitch ^=. cir. pi. X no. of teeth 

3.1416 

for diamstral pitch = no. of teeth X 1" 

dia. pi. 




Face and Flank: That part of the contour of a 
tooth which lies outside its pitch circle is called the 
Face of the tooth ; and that part which lies within the 
pitch circle is called the Flank. 



MECHANICAL DRAWING 



76 



Arc and Angle of Action. The angle throiigh 
which the wheel turns, while one of its teeth is in con- 
tact with the engaging tooth of its mate, is called the 
Angle of Action; the arc of the pitch circle, by which 
it is measured, is called the Arc of Action. The latter 
must be equal to the circular pitch, so that each tooth 
may continue in gear until the next one begins to act ; 
in practice it should be considerably greater. 

Addendum = circular pitch -^ 3 

Addendum = 1" -h diamatral pitch 

Dedendum = addendum 

Clearance = add ndum h- 8 

Tcoth = add3ndum-\-dsdjndum-\-cl3a/anc3 
Outside dia. = pi. dia. -\- 2 X addendum 

Backlash. Practically, the teeth of two engaging 
wheels are made of the same thickness ; but were 
workmanship so perfect that each tooth and space be 
made exactly equal, this would create contrary fric- 
tion and consequent loss of power ; hence, the space 
must be left a little wider than the tooth. The differ- 
ence is called Backlash, and should be as minute as it 
is practicable to m.ake it. 



Clearance. Theoretically, the depth of a space is 
equal to the distance from the addendum circle to the 
dedendum circle, but in order to let the teeth of the 
mating wheels pass the bottom of the space without 
friction, the depth of the space is made a little greater. 
The difference is called Clearance. 

Pitch Point is the mathematical point where the 
pitch circles and line of centers of two engaging toothed 
wheels meet. 

Si'UR Gears. 

1 hose ge-:'rs connecting parallel shafts and whose 
tooth elements are straight lines parallel to the axis of 
the gear. 

Rack and Pinion Gears. 

A rack may be considered as a wheel having an in- 
finite dian-.eter. The pitch line of a rack is, therefore, 
a straight line, and for every revolution of the pinion 
the rack will travel a distance equal to the circumfer- 
ence of the pinion. 



f 



i 



MECHANICAL DRAWING 



77 



SYSTEMS OF GEARING. 

There are two systems of gearing, known as -lie 
involute, or sirgle curve system, and the cycloidal, or 
double curve system. 

THE CYCLOIDAL SYSTEM. 

In mathematics a cycloid is the path described by a 
point on the circumference of a circle as the circle rolls 
upon a str^.ight line. The circle is called the gciicrc.ting 
circle. When the gencr?.ting circle rolls upon the out- 
side of another circle the curve described by any poi:it 
on the generating circle is called an cpi:ycloid. If the 
generating circle rolls on the inside of another circle, 
the curve generated by any point on the circumr(.renco 
of the generating circle is called the hypocyclcid. If the 
diameter of the generating circle is just one-half of the 
circle inside of which it rolls, the hypocycloid will be a 
straight line. 

In drawirg epic_\'cloidal teeth it is necessary that the 
diameter of the generating circle should be the same 
for all gears running together. The diameter of the 
generating circle should be equal to the radius of the 
pitch circle of a gear of 12 teeth of the given pitch, .so 



that the 12-tooth gear has radial flanks. 

To Dr.\w the Epicycloidal Tooth. 

From any point (a) on the pitch circle draw the 
epicycloid and hypocycloid curves, as in Fig. 5. Lay oiif 
circular pitch on pitch circle and draw addendum, de- 
dendum and clearance circles. The part of the curved 







GUtlire between the addendum and dedendum circles is 
the outline of the cycloidal tooth. Find center line of 
tooth ar.d draw it in the opposite side of tooth by meas- 



L.ofC. 



1 

i 



MECHANICAL DRAWING 



78 



uring from the center line of tooth : — the tooth is 
rounded into the clearance line by drawing an arc of a 
circle with radius equal to the clearance. 

Prob. 1 Draw outline of 1 tooth of a gear that 
has 18 teeth, 3" cir. pi., epicycloidal form. 

Prob. 2 Draw outline of 3 taeth of 24th. gear 
and 3 teeth of 12th. pinion in mesh, 2" cir. pi., 
epicycloidal form. 

THE INVOLUTE SYSTEiM. 

Mechanically the imolnte is the curve that would 'oe 
drawn by a pencil point at the end of a thin band that 
will not stretch and that is drawn tight while being un- 
wound from a cylinder. 

The Standard Involute Tooth is the interchangeable 
tooth having an angle of action of fifteen degrees to a 
line perpendicular to the line of centers of a pair of 
gear wheels. 

The Base Circle is the circle to which the involute 
that forms the outline of the tooth is drawn. The ra- 
dius of the base circle is sm.aller than that of the pitch 
circle, and is found by drawing a circle tangent to the 



Hne of action. 

The Face of the involute tooth is formed by the in- 
volute curve from the base circle to the addendum 
circle. 

The Fk.nk of the involute tooth is a straight radi'il 
line from base circle to the dedendum circle and round- 
ing it into the clearance circle — See Fig. 6. 
l^o Draw the Involute Tooth. 

15=^ 




Draw in order the pitch circle, line of action, radius 
of base circle, base circle, involute curve from base 



MECHANICAL DRAWING 



79 



circle, and radial flank of tooth. Then draw, in order, 
the addendum, dedcndnm, and clearance circles ; lay off 
the circular pitch, on pitch circle ; find center line of 
tooth, and draw in opposite side of tooth by measur- 
ing from the center line of tooth. 

Prob. 3 Draw ouiline of 3 tid'. of 16th. g ar 
and 3 teeth of 12th. pinion in mesh, 1 dia. pi., 
involute form. 

ODONTOGRAPHS. 

The construction of the gear tooth is not always ac- 
complished by finding points through which the curvV 
should pass and then drawing the curve through these 
points ; but the tooth outline is found by means of an 
odontograph. 

An odontograph is a method or an instrument for 
simplifying the construction of the curve, generallv b\- 
finding centers for approximating circular arcs with- 
out finding points on the curve. 

The most practical and accurate methods of approx- 
im.ating the involute and cycloidal curves by means of 
circular arcs are those devised bv Mr. ueorge P>. 
Grant, and called Grant's Odontograph. 

Note:- The Odontograph Tables and notes are from "Gran' 



Gr.\nt's Cycloid.\l Odontogr.xph. 



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The lergths of the radii of the arcs and the location 
of their cer.ters are determined by the pitch and tiie 
nun ber of teeth of the gear, in conjunction with a table 
of factors that apply to gears of all sizes from a lo 
tooth pinion to a rack. 

's Treatise on Gear Wheels" by permission from Mr. Grant. 



MECHANICAL DRAWING 

The base of the odontograph is a describing circle 
whose diameter is equal to the radius of the 12-tooLh 
pinion. A gear Hue laid out by its use will, therefore, 
work satisfactorily with any gear having the same 
pitch and general tooth dimensions, and with theoreti- 
cal curves constructed with a describing circle whos- 
diameter is equal to the radius of a 12-tooth pinion. 

After drawing the pitch, addendum, dedendum and 
clearance circles and spacing the pitch circle for the 
teeth, the circles on which lie centers of the arcs (Sec 
Fig. 7) are to be laid out. These circles are concentric 






^^^^"^#^^^24^ 




with the pitch circle, and their distances from the pitch 
circle are found from the odontograph table. 

To find the distance from the pitch circle, for the 



BO 

line of face centers for a diametrical pitch gear, use tlie 
run-.bcrs headed "Diametrical Pitch." and select froni 
the column headed "Distances A," under the heading 
"Faces," the number in the same horizontal line as 
the number corrcspondirg to the number of teeth in the 
ge.ir, which is found in the column headed "Nmnber of 
Teeth." Ibis number divided by the diametral pitch 
gives the distance in inches from the pitch circle to the 
circle of face centers. The distance "B" from the pitcli 
circle to the circle of flank centers is found by dividing 
the number in the column headed "Distance B" undjr 
the heading "Fh.nks" and in the same horizontal line 
as the number corresponding to the number of teeth in 
the gear, by the diametral pitch. 

For a circular pitch gear, the numbers headed, 
"Multiply by the Circular Pitch" are to be used, and 
the several distances and radii are formed by multiplv- 
ing the numbers by the circular pitch. 

Prcb. 4 Draw 22th. spur, and 10th. pinion 
g:ars 3 dia. pi., epicycloid a I form, using the 
Grant Odvntcgraph. Gears ara 2'/ face, and 
ksyjd on /|" shafts. 



MECHANICAL DRAWING 



81 



Grant's Odontograph for the Involute System. 
To draw the tooth, lay off the pitch, addendum, dc- 



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dendum and clearance lines, and space the pitch line for 
the teeth. Draw the base line one-sixtieth of the pitjh 
diameter inside the pitch line. Take the tabular face 
radius, after multiplying or dividing as is required by 
the table, and draw in all the faces, from the pitch line 
to the addendum line from centers on the b:ise line. 
Take the tabular flank radius, and draw in all the flanks 
from the pitch line to the base line. Draw straight 
radial flanks from the base line to the root line, and 
round them into the clearance line. (See Fig. 8.) 




F/3.S. 



Special Rule for the Involute Rack. 

Draw the sides of the rack tooth as straight lines to 
tlie line of centers "coc" at an angle of 15°. Draw the 
oulcr half "ah" of the face, one quarter of the whole 



MECHANICAL DRAWING 



82 



length of the tooth, from a center on the pitch line, and may best be drawn by joints, for the odontographic 
with a radius of 2.10 inches dizidcd by the diametr:d tooth is not so well adapted to the place as the true 
pitch .67 inches multiplied by the circular pitch. 

The construction of the rack is shown in Fig. 8. 
Annular or Internal Gears. 



//y.9 




Internal Gears are those having teeth cut inside of 
the rim. Use the involute odontograph for the internal 
gear exactly the same as for external gears ; but care 
must be taken to cut off the tooth at the interference 
point "i" of the pinion (See Fig. 9). The point of the 
tocth may be left off altogether or rounded over to give 
the appearance of a long tooth. The pinion tooth may 
be filled in and jvist clear the truncated tooth of the 
gear. The curves of the internal tooth and its pinion 



tooth, and no correction is needed for interference in 
the true tooth outlines. 

Prob. 5 Draw 25th. spur, 17th. pinion, and 
rack gears 4 dia. pi., invoiuta form, using the 
Grant Odontograph. Gears are 2\" face, and 
keyed on shafts. 




MECHANICAL DRAWING 



83 




Prob 6 Draw intarnal, and pinion gears, 3 
dia. pi., 27 and 14 taeth, invoiuta form, using 
the Grant Odontograph. 



Bevel Gears. 

In drawing spur gears in the epicycloidal system, the 
tooth curves are generated by rolHng generating cylin-' 
ders upon pitch cyhnders. In bevel gearing the pitcli 
surfaces are cones which when in rolhng contact have 
their apexes in a common point ; and it may be assumed 
that the tooth surfaces are generated by generating 
cones rolHng upon the pitch cones. 

In spur gearing the teeth of the two gears bear along 
a straight line perpendicular to the plane of the p'lper. 
In bevel gearing the teeth are in contact along straight 
lines, but these lines are perpendicular to the surface 
of a sphere, and all of them pass through the center of 
the sphere, which is at the point where the apexes of 
the two pitch cones meet. 

In Fig. lo let C i? represent a pitch cone, the part 
C D E B being the pitch surface of the bevel gear and 
let ^ O C be the generating cone. If we suppose the 
generating cone describes the tooth surface m n o p, :ov 
rolling upon the ritch cone, the line n o repTsenting 
the outer edge of the tooth will lie upon the surface of 
a sphere wbo.^e radius is o n; for the point n which 
describes this li'^e is always at a fixed dist.nnce from 
the center o, herce every point on the line n — o is 



MECHANICAL DRAWING 



84 



equally distant from o, and in a spherical surface every faces being represented hy A B C and C U E in the 
point is equally distant from a point within called the figure. 'ihe length of the arc // i? C is equal to the 
center. It therefore follows that n — o must lie upon a circumference of the pitch circle A' C, and the arc 
spherical surface. C D E is equal to the circumference of the pitch circle 

a C E'. The gear teeth are then d'-awn upon the devel- 

oped surfaces precisely as for ihe spur gears of the 
same pitch and diameter. 

t ■ 




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To be theoretically exact, the tooth curves should be 
traced upon the surface of a sphere, as shown in Fis^-. 
II. This method is not practical, however, and has 
no advantage over what is known as Tredgold's ap- 
proximation, which is much simpler and is universallv 
used. By this method the tooth curves are drawn on 
cones tangent to the spheres at the pitch lines of the 
gears, as shown in Fig. 12. The process is simply to 
develop the surface of the cones, the developed sur- 




The method of laying out the bevel gear blank is 
shown in Fig. 13. 



MECHANICAL DRAWING 



85 




- To c/rot^ t:he Be:/e/ Gec^r — 

Oroti^/. ' ce/7te/^///7e s o/7c/ /C'ri7es/io//t/? c/zome/b/s 
Z: co/7ep//c^ //>7es- /oc - oc o/7d fyc 
3- fooc/( r/fT? //'rte r-/' '- p erpe/rc/zcWor rape 

B- ii/'i^ f-r' OS ce/p/e/s c/r-gu/' O/'cs. of oc/c/e/^o'(//f7. 
^ frof^trm /me /s /3ora//e/ ti/M bac/inm///^fr 



MECHANICAL DRAWING 



86 




Prob. 7 Draw a pair of miter gears, 18tfi. 
4 dia. pi. using the Grant Involute Odontcgraph. 



Prob. 8 Draw a pair of bevel gears, 22 and 
16th., 4 dia. pi., shaft angle, 75°, using the 
Grant Involute Cdontograph. 



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